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{{About|transmission through a ''volume''|transmission through a ''surface''|Fresnel equations}}
{{About|transmission through a ''volume''|transmission through a ''surface''|Fresnel equations}}
[[File:Beer lambert1.png|thumb|240px|Diagram of Beer-Lambert Law of transmittance of a beam of light as it travels through a [[cuvette]] of width ''l''.]]
[[File:Beer lambert1.png|thumb|240px|Diagram of Beer-Lambert Law of transmittance of a beam of light as it travels through a [[cuvette]] of width ''l''.]]
[[File:Atmospheric.transmittance.IR.jpg|thumb|Earth's atmospheric transmittance over 1 nautical mile sea level path (infrared region<ref>{{cite web|url=http://web.archive.org/web/20010913091738/http://ewhdbks.mugu.navy.mil/EO-IR.htm#transmission|title=Electronic warfare and radar systems engineering handbook}}</ref>). Because of the natural radiation of the hot atmosphere, the intensity of radiation is different from the transmitted part.]]
[[File:Atmospheric.transmittance.IR.jpg|thumb|Earth's atmospheric transmittance over 1 nautical mile sea level path (infrared region<ref>{{cite web|url=http://ewhdbks.mugu.navy.mil/EO-IR.htm#transmission |title=Electronic warfare and radar systems engineering handbook |deadurl=unfit |archiveurl=https://web.archive.org/web/20010913091738/http://ewhdbks.mugu.navy.mil/EO-IR.htm#transmission |archivedate=September 13, 2001 }}</ref>). Because of the natural radiation of the hot atmosphere, the intensity of radiation is different from the transmitted part.]]
[[File:Ruby transmittance.svg|thumb|240px|Transmittance of ruby in optical and near-IR spectra. Note the two broad blue and green absorption bands and one narrow absorption band on the wavelength of 694 nm, which is the wavelength of the [[ruby laser]].]]
[[File:Ruby transmittance.svg|thumb|240px|Transmittance of ruby in optical and near-IR spectra. Note the two broad blue and green absorption bands and one narrow absorption band on the wavelength of 694 nm, which is the wavelength of the [[ruby laser]].]]



Revision as of 20:32, 2 April 2016

File:Beer lambert1.png
Diagram of Beer-Lambert Law of transmittance of a beam of light as it travels through a cuvette of width l.
Earth's atmospheric transmittance over 1 nautical mile sea level path (infrared region[1]). Because of the natural radiation of the hot atmosphere, the intensity of radiation is different from the transmitted part.
Transmittance of ruby in optical and near-IR spectra. Note the two broad blue and green absorption bands and one narrow absorption band on the wavelength of 694 nm, which is the wavelength of the ruby laser.

Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field.[2]

Internal transmittance refers to energy loss by absorption, whereas (total) transmittance is that due to absorption, scattering, reflection, etc.

Mathematical definitions

Hemispherical transmittance

Hemispherical transmittance of a surface, denoted T, is defined as[3]

where

  • Φet is the radiant flux transmitted by that surface;
  • Φei is the radiant flux received by that surface.

Spectral hemispherical transmittance

Spectral hemispherical transmittance in frequency and spectral hemispherical transmittance in wavelength of a surface, denoted Tν and Tλ respectively, are defined as[3]

where

Directional transmittance

Directional transmittance of a surface, denoted TΩ, is defined as[3]

where

  • Le,Ωt is the radiance transmitted by that surface;
  • Le,Ωi is the radiance received by that surface.

Spectral directional transmittance

Spectral directional transmittance in frequency and spectral directional transmittance in wavelength of a surface, denoted Tν,Ω and Tλ,Ω respectively, are defined as[3]

where

Beer–Lambert law

By definition, transmittance is related to optical depth and to absorbance as

where

  • τ is the optical depth;
  • A is the absorbance.

The Beer–Lambert law states that, for N attenuating species in the material sample,

or equivalently that

where

Attenuation cross section and molar attenuation coefficient are related by

and number density and amount concentration by

where NA is the Avogadro constant.

In case of uniform attenuation, these relations become[2]

or equivalently

Cases of non-uniform attenuation occur in atmospheric science applications and radiation shielding theory for instance.

SI radiometry units

Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol
Radiant energy Qe[nb 2] joule J ML2T−2 Energy of electromagnetic radiation.
Radiant energy density we joule per cubic metre J/m3 ML−1T−2 Radiant energy per unit volume.
Radiant flux Φe[nb 2] watt W = J/s ML2T−3 Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called luminosity in Astronomy.
Spectral flux Φe,ν[nb 3] watt per hertz W/Hz ML2T −2 Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1.
Φe,λ[nb 4] watt per metre W/m MLT−3
Radiant intensity Ie,Ω[nb 5] watt per steradian W/sr ML2T−3 Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity.
Spectral intensity Ie,Ω,ν[nb 3] watt per steradian per hertz W⋅sr−1⋅Hz−1 ML2T−2 Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is a directional quantity.
Ie,Ω,λ[nb 4] watt per steradian per metre W⋅sr−1⋅m−1 MLT−3
Radiance Le,Ω[nb 5] watt per steradian per square metre W⋅sr−1⋅m−2 MT−3 Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity".
Spectral radiance
Specific intensity
Le,Ω,ν[nb 3] watt per steradian per square metre per hertz W⋅sr−1⋅m−2⋅Hz−1 MT−2 Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity".
Le,Ω,λ[nb 4] watt per steradian per square metre, per metre W⋅sr−1⋅m−3 ML−1T−3
Irradiance
Flux density
Ee[nb 2] watt per square metre W/m2 MT−3 Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral irradiance
Spectral flux density
Ee,ν[nb 3] watt per square metre per hertz W⋅m−2⋅Hz−1 MT−2 Irradiance of a surface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (1 Jy = 10−26 W⋅m−2⋅Hz−1) and solar flux unit (1 sfu = 10−22 W⋅m−2⋅Hz−1 = 104 Jy).
Ee,λ[nb 4] watt per square metre, per metre W/m3 ML−1T−3
Radiosity Je[nb 2] watt per square metre W/m2 MT−3 Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral radiosity Je,ν[nb 3] watt per square metre per hertz W⋅m−2⋅Hz−1 MT−2 Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity".
Je,λ[nb 4] watt per square metre, per metre W/m3 ML−1T−3
Radiant exitance Me[nb 2] watt per square metre W/m2 MT−3 Radiant flux emitted by a surface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity".
Spectral exitance Me,ν[nb 3] watt per square metre per hertz W⋅m−2⋅Hz−1 MT−2 Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity".
Me,λ[nb 4] watt per square metre, per metre W/m3 ML−1T−3
Radiant exposure He joule per square metre J/m2 MT−2 Radiant energy received by a surface per unit area, or equivalently irradiance of a surface integrated over time of irradiation. This is sometimes also called "radiant fluence".
Spectral exposure He,ν[nb 3] joule per square metre per hertz J⋅m−2⋅Hz−1 MT−1 Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m−2⋅nm−1. This is sometimes also called "spectral fluence".
He,λ[nb 4] joule per square metre, per metre J/m3 ML−1T−2
See also:
  1. ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
  2. ^ a b c d e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
  3. ^ a b c d e f g Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek letter nu, not to be confused with a letter "v", indicating a photometric quantity.)
  4. ^ a b c d e f g Spectral quantities given per unit wavelength are denoted with suffix "λ".
  5. ^ a b Directional quantities are denoted with suffix "Ω".

See also

References

  1. ^ "Electronic warfare and radar systems engineering handbook". Archived from the original on September 13, 2001. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  2. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Transmittance". doi:10.1351/goldbook.T06484 Cite error: The named reference "GoldBook" was defined multiple times with different content (see the help page).
  3. ^ a b c d "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.